Computer Simulation of Load Equivalence Factors

Transcription

1 192 TRANSPORTATION RESEARCH RECORD 1286 Computr Simulatio of Load Equival Fators w. J. KENIS AND. M. COBB AASHTO's load quival fators ar valuatd with th aid of a omputatioal modl for prditig flxibl pavmt rspos. First th VESYS 5 omputr program was vrifid to assur that it o~ld b usd to odut omputr road tsts. Followig this, damag produd by strig axls at th AASHO Road Tst was valuatd i a ffort to quatify th rror i th AASHTO quival fators, baus strig axls wr gltd i th dvlopmt of ths quivalis. Nxt, th o~putr modl was usd i th odut of omputr road tsts with th goal of dvlopig quival fators for odi!ios ~t pr.st at ~h AASHO road tst sit. Fially, xpotial rlat1sh1ps rlatmg pavmt dfltios ad strais to load quivalis basd o rakig ad ruttig wr dvlopd. Traffi volum, vhil wight, spd, tir prssur, axl spaig, ad vhil suspsio ar fators that must b osidrd wh studyig pavmt rspos. Addd to ths ar viromtal oditios that ostatly hag, iflitig damag to th pavmt. Matrial proprtis of flxibl pavmts, for xampl, ar iflud ot oly by tmpratur, but also by vhil spd. Thus, it is tmptig for th pavmt gir to mak simplifyig assumptios i pavmt dsig, rduig th umbr of variabls to thos that sigifiatly afft pavmt rspos. O suh simplifyig assumptio ivolvs th opt of th quivalt sigl axl load (ESAL) ad load quival fator (LEF). It allows th dsig gir to rdu th umrous vhils travlig o th road to a quivalt umbr of sigl axls. Th opt was first dvlopd from th AASHO Road Tst rsults ad has b i ommo us si. Baus th data from th AASHO sit ar limitd to th oditios at th sit, it is dsirabl to ivstigat thos fators ot studid at th sit; baus th ost of odutig similar road tsts is prohibitiv, it boms oomially justifiabl to us omputatioal pavmt rspos modls. For xampl, tridm axl ofiguratios, ow ommo o th atio's highways, wr ot iludd i th AASHO Road Tst traffi. Othr fators ot studid ilud axl spaigs, vhil spaigs, trasvrs positios of th vhils o th pavmts, truk spd, ad tir prssurs. I additio, strig axls wr gltd i th dvlopmt of load quival fators (xpt for vhils havig just two sigl axls). This papr iluds th rsults of th followig rsarh objtivs. W. J. Kis, FHWA, HNR 2, 63 Gorgtow Pik, MLa, Va C. M. Cobb, Dpartmt of Civil Egirig, Louisiaa Th Uivrsity, Rusto, La Calibrat th VESYS S program to simulat th rspos masurd at th AASHO Road tst. Evaluat pavmt rspos ausd by strig axls i th AASHO Road Tst xprimts. Calulat LEFs basd o srviability ad damag. Evaluat rlatioships btw primary rspos LEFs ad damag-basd LEFs. EQUIV ALENCY CONCEPTS At th AAS HO Road Tst sit a umbr of idtial thikss dsigs wr usd i various loops so that a sigl dsig was idpdtly subjtd to svral diffrt traffi loadigs. T diffrt vhil typs (Figur 1) wr usd i th tst. Oly o vhil typ was usd i ah la so that ah pavmt stio was subjtd to oly o typ of loadig. Th distributio of vhils was suh that axl load appliatios aumulatd at th sam rat i all traffi las throughout th tst priod. Expt wh road oditios wr prohibitiv baus of pavmt distrss or wathr oditios, th vhils travld at a ostat spd of 35 mph (1). Th primary objtiv of th AASHO Road Tst was to stablish rlatioships btw pavmt prforma ad dsig haratristis suh as layr thiksss ad loadig paramtrs. Th LEFs dvlopd as a rsult of th AASHO Road Tst wr alulatd from prforma quatios basd o th rlatioship btw th umbr of load rptitios ad th prst srviability of th pavmt. A stadard sigl-axl load of 18 kips was adoptd. Th AASHTO LEF for ritria basd o prst srviability idx (PSI) is whr W is th umbr of stadard sigl axls to a limitig valu of PSI ad Wx is th umbr of ay axl (sigl or tadm) of load x to th sam limitig valu of PSI. It may also b xprssd i trms of th AASHTO prforma quatio as LEFPsi = {(Lx + L2)/(18 (1) + 1)}4.79 Li4.33 g<llplb - llpx) (2) whr Lx is th load o ay sigl or tadm axl, ~ is a futio of Lx plus th strutural apaity of th pavmt, g is a futio of th ratio of th srviability idxs ad L 2 = 1,2 th axl od for sigl or tadm axls, rsptivly (2). With th xptio of two-axl truks, th strig

2 Kis ad Cobb 193 Loop La Wight i Kips Frot Load Gross 2 Load 2 Load FIGURE 1 AASHO truks (1). Load ' g ' ' axls of th vhils wr ot osidrd to b load axls ad o provisio was mad i th road tst aalyss to study th sigifia of th strig axls o pavmt prforma. Latr, Sala (3) suggstd that th strig axls at AASHO otributd oly about 3 prt of th total damag ausd by th tst vhils. Howvr, h also suggstd that for som vhils travlig o today's highways, th strig axl arris a gratr portio of th load tha thos usd i th AASHO Road Tst ad may thrfor otribut sigifiatly to th total damag. Prviously, th AASHTO Dsig Guid iludd quivalis for oly sigl-axl loads up to 4 kips ad tadmaxl loads to 48 kips. Th latst AASHTO Dsig Guid, publishd i 1986, iluds quivals for sigl-axl loads to 5 kips, tadms to 9 kips, ad tridms to 9 kips. To obtai ths w quivalis, Equatio 2 was usd. For tridms, th axl od i Equatio 2 was giv th valu of thr. Thr is som urtaity as to th validity of xtdig ths quatios to grat quivalis for loads ad axls ot applid at th road tst. It was obsrvd by Sala (3) that th AASHTO quival fators xprssd by Equatio 1 ar approximatly qual to th fourth powr of th ratio of th atual loads: This rlatioship is ommoly kow as th Fourth Powr Law whr L taks o th stadard valus 18, 3, ad 4.7 for sigl-tadm ad tridm-axl loads. (3) I additio to prst srviability, othr pavmt rspos masurs might b usd as a basis for dtrmiig load quival fators. For damag-basd ritria (D) whr W ad Wx ar valuatd at a limitig valu of distrss rathr tha PSI, ad LEFv is kow as a damag quival fator. If o maks rtai liarity assumptios o th fl xibl pavmt fatigu rakig damag quatio, Wl = Kl(l/)K2 (5) whr Kl ad K2 ar fatigu matrial proprty ostats ad Wis valuatd at som limitig masur of rakig, th o substitutio ito Equatio 4 for th rsptiv loads, th followig primary rspos strai quival quatio is obtaid: LEF, = () )K 2 (6) I this quatio, is th tsil strai (primary rspos) for th rsptiv loads at th bottom of th AC layr. Similarly, a xprssio for primary rspos dfltio quivaly may b dvlopd by usig th rut dpth quatio (4) (7)

3 194 whr dx is pavmt maximum surfa dfltio ad µrad ar ar pavmt systm prmat dformatio proprtis. Equatio 4 may b usd i Equatio 7 to yild Caadi.a rsarh rgrssd rboud dfltio (d) agaist umbr of load rptitios to limitig PSI ( 4) to obtai whr b is th rgr sio offiit from variou. fi ld xprimts. Baus Equatios 6, ad 9 ar futi s of strai or dfltio, thy ar alld primary rspos quivalis. W a solv for th xpot i ay of Equatio 6, 8, or 9; howvr, it is mor lightig to dvlop a gral xprssio Q = log LEF/log (PR)PR ) (1) whr Q is th xpot llar, b, or K2; PR is th dfltio or strai primary rspos; ad j is a idtifir for PSI, rakig, or ruttig. This xprssio is awkward wh th primary rspo ratio or th LEF is los to or qual to 1. O othr major or with th abov quivalis is that of dfijog dx or x for multipl-axl ofiguratio. For ista, Caada has dfid dx i Figur 2 for multipl axls whr (8) (9) (11) d;, T; = pak dfltio ad trough of axl i for a axl group, (d;+ 1 - T;) diffr i magitud btw th maximum dfltio rordd udr ah sudig axl ad th miimum rsidual dfltio prdig th axl, ad TRANSPORTATION RESEARCH RECORD 1286 d = pavmt surfa dfltio ausd by th stadard sigl-axl dual tir load. A similar approah is u d i VE YS 5. Th primary trai or dfltio rspos at ay p it i th pav mt <1u d by multipl axl is obtaid through uprpositio of th rspo. at that poit au d by ah axl i th multiplaxl ofiguratio. h proportioal amout of pak to vally, as how i Figus 2, dtrmis th magitud f th rspos to b usd i th rpatd load damag modls. For xampl, for tadm axls th quatio would b Rspos 1 Rspos 2 max [d 1, d1] mi [d 1, d 1 ] - T 1 (12) Th algoritl gralizs radily to highr multipl-axl groups. This produr diffrs from th aadia m thod i that it assigs o spial tratmt to th lad axl i th axl group. Rathr, it assums that th gratst damag is ausd by th grat st rspos, rgardlss of whih axl appars to b produig that rspos. VESYS COMPUTATIONAL MODEL Th volutio of th VESYS sris of omputatioal pavmt modls bga i th mid-197s with th dvlopmt of a prototyp vrsio, VESYS 2M, a dosd form thr-layr visolasti modl (5). Si th dvlopmt of VESYS 2M, t othr vrsios hav b produd (6). Giv paramtrs that dfi th pavmt, viromt, ad loadig, YESYS a prdit th pavmt's bhavior ovr tim. Iitially, layr thory is usd to alulat primary rspos strss, strai, ad dfltio udr a stati loadig. Ths valus ar usd alog with traffi loadig i umulativ damag modls to prdit rakig, ruttig, ad roughss. Fially, th prst srviability idx is omputd..7 s.6 u r f.5 a.4 D f.3 I t.2 i.1 FIGURE 2 Tadm axl.

4 Kis ad Cobb 195 VESYS 5 has th uiqu fatur of aalyzig pavmt rspos ausd by sigl, tadm, or tridm axl loadigs. Traffi volums ar spifid i AADT (avrag aual daily traffi) whri ah axl group is osidrd to b o ompot of th traffi. Th atual vhil ofiguratio may osist of svral axl groups up to thr axls. Eah group is outd sparatly i th AADT dsigatio. Th usr also spifis th umbr ad lgth of tim priods ito whih th traffi flow ovr th tir aalysis priod is dividd. Th prtag of ah axl group omposd i th AADT is spifid ad may b adjustd for sasoal variatio (B. Bradmyr, upublishd FHWA data). VERIFICATION AND CALIBRATION Ay wly dvlopd omputatioal pavmt modl must first b vrifid for ralisti rags of viromtal, matrial, ad traffi paramtrs. O it is vrifid, th modl a b alibratd so that prditios of pavmt rspos ar withi a dsirabl dgr of auray for a spifi st of oditios. Calibratio may b do ithr itrally or xtrally (7). Itral alibratio is arrid out by adjustig program iputs (usually matrial proprtis). Extral alibratio is ahivd by applyig a alibratio fator to th program output. Most of th mhaisti modls omprisig VESYS 5 ad usd i this study wr vrifid ad alibratd for AASHO oditios i prvious studis. Howvr, i this study VESYS 5 is furthr alibratd itrally by omparig rsults of damag prditios with masurd valus of ruttig, rakig, ad srviability from th 16 AASHO Road Tst stios show i Tabl 1. Th stios wr sltd so that two thikss dsigs ould b aalyzd ovr th tir rag of loadig ofiguratios for th mai loops (3 through 6). A study odutd by Kis t al. (8) i 1982 dvlopd valus for layr stiffss moduli, prmat dformatio proprtis (GNU ad ALPHA), ad fatigu proprtis Kl ad K2 for four sasos. Ths valus ar show i Tabl 2 ad wr applid to dtrmi iputs for VESYS 5 for us i th alibratios. Th traffi rats applid to VESYS (for th alibratios) wr kpt idtial to th rats applid at th AASHO tst sit. Sasoal Data YESYS 5 has th apability of modlig viromtal hags at variabl itrvals of up to 12 sasos pr yar. Primary rspos is gratd for ah saso. Dtrmiatio of th umbr ad lgth of sasos was do by aalysis of dfltio masurmts tak at th AASHO Road Tst vry 2 wks. Ths dfltios wr avragd for th 2-yar priod ad ar plottd as show i Figur 3. Th viromtal hag havig th gratst fft o dfltios is th sprig thaw, bgiig aroud Marh 18 ad dig aroud May 13. Pavmt tmpraturs for ah saso wr obtaid by addig 24 F to th avrag air tmpratur for ah of fiv sasos, as suggstd by Rauhut ad Jordahl (9). It was dtrmid from this plot that th oditios at th AASHO Road Tst ould adquatly b modld with th fiv sasoal itrvals show. Layr Stiffss Moduli Adjustmts wr mad to th stiffss moduli of Tabl 2 so that thy would orrspod with th sasos sltd for YESYS 5. Th fial valus usd for th study ar giv i Tabl 3. Th surfa layr rp omplia urv show i Figur 4 was usd alog with th tim tmpratur shift rlatioship (8): whr (13) t 7 = tim orrspodig to th omplia at rfr tmpratur T, TABLE 1 MAIN DESIGNS FOR AASHO LOOPS 3 THROUGH 6 AAS HO Axl Axl AASHO Stio Numbr* LOOP Typ Load (pouds) D.s ig Ds ig 3 Sigl 12, Tadm 24, Sigl 18, Tadm 32, Sigl 22, Tadm 4, Sigl 3, Tadm 48, * Surf a-8as-subbas Thikss, ihs

5 TABLE 2 MATERIAL PROPERTIES USED BY KENIS ET AL. (14) Matrial Witr Sprig Summr Pro rt Modulus (KSI) Surfa Bas Subbas Subgrad Prmat Dform Surf a GNU ALPHA Bas GNU Variabl Futio of Strss ALPHA Subbas GNU Variabl Futio of Strss ALPHA Subgrad GNU ALPHA Fatigu Surf a Kl 1.E-13 l.8e E-8 K Fall E Ma Dfltio Thousodt hs of Ihs Saso 1 15 days 5 dgrs Saso 2 57 days 69 dgrs Saso 3 7 days 9 1 dgrs Saso 4 7 days 97 dgrs Saso 5 63 days 75 dgrs f--"'--_.. -l---'--'--+--'-..l..l--+---'~'-'-+--_....._-+-_._l-'---+--'----'---+-'-''--"' ' 12/3 1/14 2/25 4/7 5/19 5/3 8/1 1 9/22 11/3 Dat FIGURE 3 AASHO loop I.

6 Kis ad Cobb TABLE 3 SEASONAL LA YER MODULI Moduli (ksi) for Saso Saso Saso Saso Saso Surfa 1, Bas Sub bas Sub grad NOTE: Saso 1: 15 days, 5 F; saso 2: 57 days, 69 F; saso 3: 7 days, 91 F; saso 4: 7 days, 97 F; ad saso 5: 63 days, 75 F. tr = tim orrspodig to th sam omplia o shiftd urv at tmpratur T, ad ar = tim tmpratur shift fator = lq(ro-t)~ Th tim fro o th mastr rp omplia urv of Figur 4 for ay tmpratur T (with tr stimatd to b.3) is obtaid by fro = (.3)1Q(r-7)~ (14) whr 13 =.54 as rommdd by Rauhut ad Jordahl (9). To obtai th surfa stiffss moduli, th omplia for ah tmpratur is tak from th mastr rp omplia urv ad ivrtd. For th sprig saso, bas ad subbas stiffss moduli wr obtaid from omographs foud prviously (1). Rsults from CBR tsts (11) tak bfor plamt of th pavmt at th AASHO Road Tst wr usd to stimat sprig subgrad moduli. For th rmaiig sasos, bas, subbas, ad subgrad stiffss moduli wr obtaid by adjustig th valus sltd for sprig usig svral diffrt produrs, viz., sasoal multiplirs ad bak alulatios usig dfltio basis masurd at th AASHO Road Tst (2). Layr Prmat Dformatio Proprtis Th rsults of rpatd load tsts odutd by th FHW A o a otrol mix of asphalt ort at 4 F, 75 F, ad 9 F Crp Complia (1/psi) 1.E-4 ~----'----' E-5 1.E-6 1. OE -7 '----'--L.L..L..u..u.L--'---'-J...LIUJ.L'---'--'-.u..Ju..u...._... u,;,l.1 O.Q1.1 1 Tim (sods) FIGURE 4 Road tst surfa (8). wr usd to obtai valus of ALPHA ad GNU for th surfa layr for iput to VESYS 5 (8). Valus of GNU for th bas ad subbas i th Kis t al. study (8) wr stablishd as futios of dviator strss. Howvr, a rt study by Lahy (upublishd FHWA data) showd that dviator strss has littl iflu o GNU for ths layrs. Prlimiary rus for th urrt study supportd Lahy's olusio. Th ALPHA valus for th bas ad subbas, wh varid, wr foud to hav littl iflu o pavmt rspos for all sasos ( 8). Data from th AASHO Road Tst (11) idiat that th moistur ott i th subgrad was about 14 prt for th sprig ad 12 prt for th othr sasos. Th rlatioship btw GNU ad moistur ott for th subgrad is plottd i Figur 5. Th fft of moistur ott o ALPHA for th subgrad has ot b stablishd. Th iitial valus from th study by Kis t al. (8) wr usd to mak adjustmts through trial ad rror util rasoably good prditios of ruttig wr obtaid. Tabl 4 shows fial valus of GNU ad ALPHA usd i this study. Fatigu Proprtis Fatigu proprtis (Kl ad K2) for th surfa layr hav b stablishd at 7 F to b approximatly 2. x 1-12 ad 5., rsptivly (9). Sasoal adjustmts to ths valus wr mad usig adjustmt fators giv i th VESYS usr's maual (5). Agai, alibratio was obtaid through trial ad rror by omparig masurd valus of rakig with VESYS 5 prditios. Valus of Kl ad K2 usd for th surfa layr i th quivaly aalysis ar as follows: Saso 1 Saso 2 Saso 3 Saso 4 Saso 5 Kl 6. x x x x x 1-11 K Calibratio Simulatios Th xampls of pavmt rspos giv i Figur 6, ar vid of rasoabl prditios of ruttig (a), rakig ( b), ad srviability for sigl ad tadm axls () at AASHO. Ir ad outr whl path damag ar vid of a high GNU / v ---- ~ Prt Moistur FIGURE 5 Subgrad GNU (8). / I/ I/ I

7 198 TRANSPORTATION RESEARCH RECORD 1286 TABLE 4 SEASONAL LAYER PERMANENT DEFORMATION PROPERTIES GNU/ALPHA Saso 1 Saso 2 Saso 3 Saso 4 saso 5 Surf a Bas.45.1 ' Subbas Subgrad dgr of variability as idiatd i th plots. Cosidrig that th sasoal matrial proprtis for all stios ar rprstd by a sigl valu, dviatios from masurd data ar xptd. It is itrstig to ot that th dviatios btw masurd ir ad outr whl path oft ar gratr tha dviatios btw VESYS ad ay o of th masurd valus. Th rsults of ths simulatios stablish VESYS as a suitabl tool for aalysis of th mai objtivs of this study. ANALYSIS To study th mai objtivs, a sigl pavmt dsig (orrspodig to AASHO stios 121, 122, 269, ad 27 of loops 3 ad 6) havig surfa, bas, ad subbas thiksss of 4, 3, ad 8 i., rsptivly, was sltd. Axl loads ad tir prssurs usd ar giv i Tabl 4. Thy wr sltd so that th otat radii ragd from 5 to 8 i. (whih also orrspods to th rag for AASHO vhils). Th AASHO traffi rats wr usd i VESYS for th strig axl aalysis; howvr, adjustmts wr mad to ths rats for th LEF damag ad primary rspos aalyss. Strig Axl Aalysis To study th validity of gltig strig axls i th dvlopmt of AASHTO LEFs, ah of th four vhils show i Figur 1 for loops 3 ad 6 was applid i a VESYS 5 simulatio both with ad without strig axls. Traffi rats idtial to thos at AASHO wr usd. A xampl of th rsultig damag prditios is giv i Figur 7 for AASHO tst stio 27. It is obvious from this plot that vry littl pavmt damag was ausd by th strig axls i th VESYS simulatio. Simulatios o th othr thr vhils produd idtial olusios. For th four stios aalyzd, avrag strig axl damag was about 2.1 prt for ruttig,.125 prt for rakig, ad 1.31 prt for srviability. Simulatio of th rmaiig stios at th road tst should yild similar rsults baus all of th strig axls supportd approximatly th sam prtag of loadig. Srviability ad Damag-Basd Aalysis Iitial omputr rus mad with th AASHO traffi rats for tridm axl ofiguratios rsultd i total loss of srviability arly i th simulatio, durig th first sprig thaw. This loss ld to quivalis for vry havy tridm axl loadigs that wr uxptdly low. Ths quivalis ar plottd i Figur 8 ad ar ompard with th AASHTO quivalis. Thus, traffi rats wr lowrd so that damag ourrd at a stabl rat throughout th simulatio priod, but th rlativ variability i traffi volum was maitaid ovr th fiv sasos. Usig th adjustd traffi rats, load quival fators basd o VESYS 5 prditios of ruttig, rakig, ad srviability wr alulatd for ompariso with AASHTO LEFs usig Equatio 1 for srviability ad Equatio 4 for ruttig ad rakig. Trmial lvls of% i. for ruttig, 5 prt for rakig, ad 3. for srviability wr usd i dtrmiig quivalis. Th alulatd quivalis ar giv i Figurs 9 through 12. Figurs 9 ad 1 ompar AASHTO LEFs to thos basd o th VESYS 5 prditios of srviability. I gral, th VESYS 5 srviability LEFs for all axl ofiguratios ar losly orrlatd with AASIITO LEPs. Mior dviatios ar appart, suggstig that quivalis basd o VESYS 5 prditios of srviability iras at a rat slightly lowr tha do AASHTO quivalis. VESYS prditios of damag-basd LEFs ar plottd i Figurs 11 ad 12. Tridm quival is plottd i Figur 11 for thr diffrt damag ritria. Th hoi of damag ritrio appars to hav a mixd fft o LEF; howvr, ruttig quivalis ar, i gral, lowr for all ofiguratios. Ruttig LEFs ar also plottd i Figur 12 but groupd aordig to axl ofiguratio istad of damag ritrio (for othr damag ritria, th plots ar similar i shap). Figur 12 suggsts th xist of a osistt rlatioship btw quivalis for multipl-axl ofiguratios. A itrstig phomo a b obsrvd from Figurs 11 ad 12. I th figurs it is appart that a wid rag of axl loads hav quivalis basd o ruttig approximatly qual to o. For ths axl loads, failur ourrd durig

8 VESYS 5 Masurd Ir Whl Masurd Outr Whl (a) ,, V hil Passs (Thousads) Ara Crokd (sq ft/1 OOOsq ft) 1,.-~~~~~~'--'---'-~~~...:...---'.~~~~~~~~~~~~ (b) VESYS 5 Masurd Ir Whl Masurd Outr Whl Vhil Poss s (Thousads) 5, Prst Srviohility Idx 4.5 VESYS 5 4. '. Masurd I r Whl () a-;-. ~...:... '... : :.1 Masurd Outr Whl 3. ' ' " 1.5 ' ' ' ' Vhil Posss (Thousads) FIGURE 6 AASHO Stio 121, pavmt 12 K sigl: (a) rut dpth; (b) ara rakd; ad () prst srviability idx.

9 Rut Dpth (ihs) 1.8 ~~~~~~~~~~~~~~~~~~~~~~~~~-, D D VESYS5 with Str -a- VESYS5 without Str O.O!!'l-~-'-~-'-~----'-~_...~ J'----~'---~-'--~--'-~-'-~----'-~--'~~ Vhil Passs (Thousads) FIGURE 7 AASHO Stio 27, pavmt 48 K tadm. E q 1. MSHO, 3. PSI VESYS 5, 3. PSI v a VESYS 5, 5% Crak I -a 1. F a t 1..1 ~~~~~~~~---'~~~~~~~~~~---'~~~ Axl Load FIGURE 8 Tridm quival (AASHO traffi rat). E q u i v a I F l MSHO, 3. PSI -+- VESYS 5, 3. PSI Axl Load FIGURE 9 Sigl-axl quival (adjustd traffi rat).

10 E q 1. MSHO, 3. PSI v a I F a 1. t VESYS 5, 3. PSI Axl Load FIGURE 1 Tridm quival (adjustd traffi rat). E q u i v a 1. I F a t 1. i= ~ VESYS 5, 3. PSI -4- VESYS 5, 5% Crak -- VESYS 5, 3/4" Rut.1 '----'---'-----'----''----'---'---'-----'--.. _,_, Axl Load FIGURE 11 Tridm quival (adjustd traffi rat). VESYS prditios of damag-basd LEFs. E q u i v a I F a t 1. i:; ~ / Sigl Axls Tadm Axls Tridm Axls.1 L---'---'-----'--~'----'---'-----' ''----'---'-' Axl Load FIGURE 12 VESYS ruttig quival (adjustd traffi rat).

11 22 TRANSPORTATION RESEARCH RECORD 1286 Rut Dpth (ihs) ~~~~~~~~~~~~~~~~~~~~~~~~~ k Sigl Axl 3 k Sigl Axl Vhi l Passs (Thousads) FIGURE 13 VESYS 5 ruttig prditios (AASHO traffi rat). th sod sprig thaw, as was th as with th 18-kip stadard. Th xist of this phomo is dsribd i Figur 13, whih shows VESYS 5 prditios of ruttig for th 18- kip stadard ad for th 3-kip sigl-axl loads. Th sharp iras i ruttig to lvls abov % i. ours at approximatly th sam umbr of rptitios (25, to 3, vhil passs) for both loads. Th quivaly for th %-i. failur lvl is 1., whras th quivaly for a Vi-i. failur lvl is muh highr at approximatly 6.. Ths xampls illustrat that th saso i whih failur ours (also a futio of traffi rat) has a importat iflu o th valu of th load quival fator. Grally, if failur ours durig th sam sasos of th sam yar for both th stadard axl load ad th load for whih th quivaly is big obtaid, th quivaly will b los to o. If failur ours for o of th axl loads durig th followig yar, th quivaly will b highr for loads gratr tha th stadard ad lowr for loads smallr tha th stadard, assumig that traffi rats ar ot altrd. It is importat to ot that from th four mai traffi loops at th road tst, 45 prt of th stios wr rmovd from th tst bfor th d of th first sprig saso. This prtag is brok dow by load as follows: Sigls 12 kip- 77% 18 kip-5% 22.4 k-37% 3 kip- 17% Tadms 24 kip-87% 32 kip-47% 4 kip-37% 48 kip-13% Th abov aalyss suggst that, had traffi rats b rdud so that all stios lastd throughout th tst priod, th AASHTO load quivalis would hav b highr for loads gratr tha th stadard ad lowr for loads smallr tha th stadard. Primary Rspos Aalysis Strai Basd-Th AASHTO ad th rakig LEFs (Figurs 9-12) wr rlatd to th strai ratios for ah of th fiv sasos ad for ah of th sigl-, tadm-, ad tripl-axl loads (Tabl 5) usig Equatio 1. Th xpot was th TABLE 5 AXLE CONFIGURATIONS USED IN LOAD EQUIVALENCE ANALYSIS S:igl!l AXl!lS Ta d m Axl s Tr idm Axl s L 2 ~!1 T1 r Pr s s ur ~ L!!ad Ilr!l f i:ll~~ u i:!l L2ad Il~ Pi-s~ur 12 kip 75 psi 24 kip 75 psi 3 kip 75 psi 18 kip 75 psi 32 kip 75 psi 36 kip 75 psi 22.4 kip 75 psi 4 kip 75 psi 46 psi 75 psi 3 kip 75 psi 48 kip 8 psi 54 kip 75 psi 4 kip 75 psi 6 kip 1 psi 6 kip 75 psi 5 kip 8 psi 7 kip 115 psi 7 kip 75 psi 9 kip 135 ps i 9 kip 75 psi 12 kip 1 psi 15 kip 135 ps i

12 Kis ad Cobb alulatd for all ass. Expots for tadm-axl rakig LEFs ar plottd i Figur 14 (similar trds wr obsrvd for sigl ad tridms). Not that th urvs td to ifiity wh th strai ratios ar los to or qual to o. Also, wh th LEF i th umrator is idtially qual to o, a udfid / oditio xists. Strai ratios los to o our wh th global maximum strai of th axl group approahs that strai produd by th 18k stadard sigl-axl load. Not that th tadm xpot is a positiv umbr at all tims. This xpot is positiv baus th umrator of Equatio 1 (log of rakig LEF) is at all tims gratr tha th domiator (log of strai ratios). A similar st of urvs (ot show) for tadms was produd usig "log of AASHTO LEF" i th umrator. Th xpots, although positiv umbrs, wr grally smallr tha thos basd o rakig simply baus th AASHO LEFs usd wr grally smallr tha th rakig LEFs. For sigls ad tridms th AASHTO LEFs grally wr largr (for itrmdiat loads) tha rakig LEFs, ad thus th xpots basd o AASHTO LEFs wr grally largr tha thos basd o rakig LEFs. This aalysis suggsts that th magitud, th bhavior, ad th typ of LEF usd i th umrator play a sigifiat rol i th powr law formulatio. Aothr qually importat obsrvatio from Figur 14 dmostrats th ssitiv atur of th powr law formulatio, spially for witr ad summr oditios. For all axl typs ad for all formulatios (AASHTO or rakig), th xpot at th itrmdiat load lvl is highr for th warmr sasos. This highr valu is dirtly attributabl to th magitud of th strai ratios usd i Equatio 1 (th LEF i th umrator as dfid for ah load is a avrag valu ovr all sasos). Thus th strai ratios i th warmr sasos (at itrmdiat load lvls) ar sigifiatly smallr tha th strai ratios i th oldr sasos. This ourr is a rsult of usig liar lasti layr thory wh th otat radius is irasd (if otat prssur rmais ostat) as load is irasd. Had otat prssur b irasd ad otat radius b hld ostat as load was irasd, th th larg diffrs btw witr ad summr strai ratios would hav b gligibl. Si otat radius dos, i fat, iras with irasig axl load, thr is justifiatio for dvlopig sasoal LEFs. Dfltio Basd-Th xpotial rlatioship btw VESYS prditios of dfltios ad AASHTO LEFs was alulatd similarly as for strai aalysis. Tridm axl xpots for witr ad summr sasos ar plottd i Figur 15. Hr th xpots ar wll-bhavd, xhibitig valus ovr all load lvls btw 3.5 ad 4; i additio, thr is littl vid of ay sasoal ffts o th xpots. Similar urvs wr obtaid for sigl ad tridms. Wh ruttig LEFs ar usd i th umrator of Equatio 1, vry rrati but ot ivalid urvs ar obtaid. Tadm xpots ar show plottd i Figur 16. A similar rasoig as applid i th strai ratio aalysis is also valid hr. Wh th LEF i th umrator is los to o, th xpot approahs zro. This rrati bhavior is solly ausd by th viromtally idud stpwis bhavior of th ruttig LEFs show i Figur 11. Agai this illustrats th major fft that traffi rat ad sasoal matrial proprty hags hav o stablishig lvls of axl quivaly. CONCLUSIONS AND RECOMMEND A TIO NS Th good agrmt btw VESYS-5 prditios of ruttig, rakig, ad PSI with masurd valus at th AASHO Road Tst is justifiatio for usig VESYS to odut xtdd road tsts ad aalyss. Th good agrmt also justifis th itral alibratio mthodology applid for th alibratio. Th strig axls at th AASHO Road Tst had virtually o iflu o pavmt rspos. Thrfor, th fat that thy wr gltd i th dvlopmt of th AASHTO load quival fator quatios is appropriat. Th rlatioship btw sasoal matrial proprtis ad traffi rat a sigifiatly iflu load quival fators. To stablish load quivalis that ar rprstativ of th tir rag of sasos, traffi rats should b adjustd so that damag ours at a fairly ostarrat throughout th tst priod. To ahiv a mor aurat stimatio of th E 42 x p t ~Witr ---*'"- Sprig thaw --*- Summr Ax l Load FIGURE 14 LEF). Strai-basd LEF xpots: tadms (basd o rakig

13 24 TRANSPORTATION RESEARCH RECORD E 4. x p t Witr Sprig thaw """"'*- Summr Axl Load FIGURE 15 LEF). Dflt-basd LEF xpots: tridms (basd o AASHO rlativ damag ausd by various vhil typs, sasoal load quival fators should b osidrd. If traffi at th AASHO Road Tst had b adjustd so that all stios lastd throughout th tst priod, th rsultig load quival fators may hav b diffrt. This iformatio is partiularly importat i light of th fat that th failur rat of stios subjtd to lightr loads was osidrably highr tha th failur rat of stios subjtd to havir loads. Ratios of strais ad dfltios raisd to a xpot a b usd to dtrmi load quival fators. Th xpots basd o strai vary with saso; xpots basd o dfltio ar similar for all sasos. Th logarithmi powr law xprssio is ssitiv to th typ, shap, ad magitud of th LEF usd i th umrator. Furthr study of th rlativ damag ausd by th various vhil typs should us "omputr tst road" simulatios to vrify th Fasibility of usig tir vhil quivalis, Efft of traffi rat o th AASHO LEF, Fasibility of sasoal load quival fators, ad Fasibility of usig primary rspos as a masur of vhil damagig ffts. ACKNOWLEDGMENTS Fiaial support for C. M. Cobb was providd through th Natioal Highway Istitut graduat rsarh fllowship program. Th iformatio was odsd ad ditd from a FHWA upublishd rport\m.s. thsis prpard by C. M. Cobb whil h was a Louisiaa Th Uivrsity, Rusto, Graduat Rsarh Fllow at th Turr Fairbak Highway Rsarh Ctr. Thial support for th study was providd i part by Pavmts Divisio, FHWA, Offi of Rsarh, Dvlopmt ad Thology Trasfr ad Dpartmt of Civil Egirig, Louisiaa Th Uivrsity. Spial thaks ar xtdd to Lsli K. Gui of Louisiaa Th Uivrsity ad to Doa Mal for hr support i produig this doumt E 4. x p t FIGURE 16 LEF). -+- Witr ""*- Sprig thaw --*- Summr Axl Load Dflt-basd LEF xpots: tadms (basd o ruttig

14 Kis ad Cobb 25 REFERENCES 1. Spial Rport 61A: Th AASHO Road Tst, History ad Dsriptio of Projt. HRB, Natioal Rsarh Couil, Washigto, D.C., Spial Rport 61 E: Th AASHO Road Tst, Rport 5, Pavmt Rsarh. HRB, Natioal Rsarh Couil, Washigto, D.C., A. J. al. ompariso of th R~s po s of Pavmts to Sigl ad Tadm Axl Loads. I Australia Road Rsarh Board: Pmdi11gs of th 5th Cofr, Cabrra, War Publishig Pty. Ltd., J. T. Christiso. Vhil Wights ad Dimsios Study, Vol. 8. I Pavmts Rspos to Havy Vhil Tst Program, Part 2, Thial Rport, Load Equivaly Fators. Roads ad Trasportatio Assoiatio of Caada, July W. J. Kis. Prditiv Dsig Produrs, VESYS Usrs Maual-A Itrim Dsig Mthod for Flxibl Pavmts Usig th VESYS Strutural Subsystm. Rport FHWA-RD FHWA, U.S. Dpartmt of Trasportatio, Jauary W. J. Kis. Th Ruttig Modls of VESYS. Pro., 25th Cofr 11 Pavig ad Trasportatio, Th Uivrsity of Nw Mxio, Albuqurqu, Jauary M. G. Sharma, W. J. Kis, ad M. Mirdamadi. Evaluatio of Mhaial Paramtrs of I-Srvi Pavmts from Fild Data. Pro., 6th Itratioal Cofr o th Strutural Dsig of Asphalt Pavmt, A Arbor, W. J. Kis, J. A. Shrwood, ad T. F. MMaho. Vrifiatio ad Appliatio of th VESYS Strutural Subsystm. Pro., 5th /111matio11a/ Cofr 11 1/1 Strutural Dsig of Asphalt Pavmts, Ui11rs.ity of Mihiga, A11 Arbor, d Dlft Ui vrsity of Thology, Dlft, Th Nthrlads, Vol. 1, August J.E. Rauhut ad P. R. Jorda.hi. Effts o Flxibl Highways of lrasd Lgal Wights U ig VESYS JIM. Rport Fl-TWA RD-77-L16, FHWA, U.. Dpartmt of Tra poatio, Washigto,..., Jouary NCHRP Rport 128: Evalua1io of AASHO Itrim Guids for Dsig of Pa vmlll Struturs. HRB Natioal Rsarh Couil, Washigto, D.C., Spial Rpo 61 B: Th AASHO Road Tst, Rport 2, Matrials a11d Costm1io11. TRB, Natioal Rsarh ouil, Washigto, D.., Publiatio of this papr sposord by Committ o Flxibl Pavmt Dsig.